对数辛流形的复形、留数和障碍
Complexes, residues and obstructions for log-symplectic manifolds
摘要：
我们考虑偶数维4或更高维的紧致Kählerian流形$X$，它具有对数辛结构$Φ$，这是一个一般非退化的闭2-形式，在具有局部正规交叉的因子$D$上具有单极点.一个简单的线性不等式，涉及迭代Poincaré残留的$Φ$的$D$的双重轨迹的组件，确保对$(X, Φ)$有通畅的变形和$D$局部平凡变形。
英文摘要：
We consider compact Kählerian manifolds $X$ of even dimension 4 or more, endowed with a log-symplectic structure $Φ$, a generically nondegenerate closed 2-form with simple poles on a divisor $D$ with local normal crossings. A simple linear inequality involving the iterated Poincaré residues of $Φ$ at components of the double locus of $D$ ensures that the pair $(X, Φ)$ has unobstructed deformations and that $D$ deforms locally trivially.
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